X619

COMPLEMENT OF X14

X619 is the complement of X14.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 618, 620 }: Central Line L(618, 620) { 2, 14 }: Central Line L(2, 14) { 13, 99 }: Central Line L(13, 99) { 16, 299 }: Central Line L(16, 299) { 39, 396 }: Central Line L(39, 396) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_618 = COMPLEMENT OF X(13) (0.5122, 0.1590) X_620 = MIDPOINT OF X(618) AND X(619) (0.4308, 0.2580) X_2 = CENTROID (0.5374, 0.2000) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_99 = STEINER POINT (0.1109, 0.4322) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_396 = MIDPOINT OF X(13) AND X(15) (0.5699, 0.2349) X_619 = COMPLEMENT OF X(14) (0.3494, 0.3571) A B C X618 X620 X2 X14 X13 X99 X16 X299 X39 X396 X619 (a, b, c) = (5, 6, 7) | AB = 1

X619 (COMPLEMENT OF X14) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = [2S_{B}S_{C} + 5S_{A}a^{2} - 2 \sqrt{3} (b^{2} + c^{2}) \operatorname{area}]/a\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(1.757337302726\)
▸ Alternate Coordinates1 form

  • Trilinears: \(F(14)/a - \csc(A - \pi /3) : F(14)/b - \csc(B - \pi /3) : F(14)/c - \csc(C - \pi /3)\)

▸ Incident Central Lines11 lines

{2, 14}, {3, 636}, {5, 630}, {13, 99}, {16, 299}, {30, 624}, {39, 396}, {62, 628}, {140, 629}, {141, 542}, {395, 533}

▸ Functional Relations10 relations